Abstract In this paper, we consider the first Steklov–Dirichlet eigenvalue of Laplace operator in annular domains with a spherical hole. We prove monotonicity result respect to hole, when outer region is centrally symmetric.

A complete characterization of the convergence factor can be very useful when analyzing the asymptotic convergence of an iterative method. We will here establish a formula for the convergence factor of the method called residual inverse iteration, which is a method for nonlinear eigenvalue problems and a generalization of the well known inverse iteration. The formula for the convergence factor ...

Let Ω be some domain in the hyperbolic space Hn (with n ≥ 2) and S1 the geodesic ball that has the same first Dirichlet eigenvalue as Ω. We prove the Payne-Pólya-Weinberger conjecture for Hn, i.e., that the second Dirichlet eigenvalue on Ω is smaller or equal than the second Dirichlet eigenvalue on S1. We also prove that the ratio of the first two eigenvalues on geodesic balls is a decreasing f...